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%I #24 Feb 01 2022 12:09:45
%S 55,726,5148,26026,105105,360360,1089088,2975544,7482618,17551820,
%T 38798760,81477396,163601438,315762216,588376800,1062347000,
%U 1864418985,3188915730,5327982660,8713054350,13970931975,21998673840,34062462720,51926743440,78021243300
%N a(n) = 11*(n+1)*binomial(n+2,11)/2.
%C Number of 14-subsequences of [ 1, n ] with just 2 contiguous pairs.
%H T. D. Noe, <a href="/A027784/b027784.txt">Table of n, a(n) for n = 9..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: 11*(5+x)*x^9/(1-x)^13.
%F a(n) = C(n+1, 10)*C(n+2, 2). - _Zerinvary Lajos_, Apr 28 2005; corrected by _R. J. Mathar_, Mar 15 2016
%F From _Amiram Eldar_, Feb 01 2022: (Start)
%F Sum_{n>=9} 1/a(n) = 5226139/158760 - 10*Pi^2/3.
%F Sum_{n>=9} (-1)^(n+1)/a(n) = 5*Pi^2/3 + 40960*log(2)/63 - 74154901/158760. (End)
%t Table[11(n+1) Binomial[n+2,11]/2,{n,9,40}] (* or *) LinearRecurrence[ {13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{55,726,5148,26026,105105,360360,1089088,2975544,7482618,17551820,38798760,81477396,163601438},30] (* _Harvey P. Dale_, May 11 2013 *)
%K nonn,easy
%O 9,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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